Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke





.......................

.......................


Publications [#235794] of Robert Calderbank

Papers Published

  1. Calderbank, AR; Jr, EGC; Flatto, L, OPTIMUM HEAD SEPARATION IN A DISK SYSTEM WITH TWO READ/WRITE HEADS., Journal of the ACM, vol. 31 no. 4 (1984), pp. 826-838 [doi]
    (last updated on 2017/12/18)

    Abstract:
    A mathematical model of computer disk storage devices having two movable read/write heads is studied. Storage addresses are approximated by points in the continuous interval left bracket 0,1 right bracket , and requests for information on the disk are processed first-come-first-served. We assume that the disk heads are maintained a fixed distance d apart; that is, in procesing a request, both heads are moved the same distance in the same direction. Assuming that successive requested locations are independently and uniformly distributed over left bracket 0,1 right bracket , we calculate the invariant measure of a Markov chain representing successive head positions under the nearer-server rule: Requests in left bracket 0,d right bracket are processed by the left head, those in left bracket 1 minus d, 1 right bracket by the right head, and those in left bracket d, 1- minus d right bracket by the nearer of the two heads. Our major objective is the equilibrium expected distance E(d) that the heads are moved in processing a request. For the problem of designing the separation distance d, we show that E (0. 44657) equals 0. 16059 equals min//dE(d). Thus, a basic insight of the analysis is that a system with two heads performs more than twice as well as a system with a single head.

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320